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Automatic estimation of multivariate spectra via smoothing splines

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  • Ori Rosen
  • David S. Stoffer

Abstract

The classical method for estimating the spectral density of a multivariate time series is first to calculate the periodogram, and then to smooth it to obtain a consistent estimator. Typically, to ensure the estimate is positive definite, all the elements of the periodogram are smoothed the same way. There are, however, many situations for which different components of the spectral matrix have different degrees of smoothness. We propose a Bayesian approach that uses Markov chain Monte Carlo techniques to fit smoothing splines to each component, real and imaginary, of the Cholesky decomposition of the periodogram matrix. The spectral estimator is then obtained by reconstructing the spectral estimator from the smoothed Cholesky decomposition components. Our technique produces an automatically smoothed spectral matrix estimator along with samples from the posterior distributions of the parameters to facilitate inference. Copyright 2007, Oxford University Press.

Suggested Citation

  • Ori Rosen & David S. Stoffer, 2007. "Automatic estimation of multivariate spectra via smoothing splines," Biometrika, Biometrika Trust, vol. 94(2), pages 335-345.
    • Handle: RePEc:oup:biomet:v:94:y:2007:i:2:p:335-345
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    File URL: http://hdl.handle.net/10.1093/biomet/asm022
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    Citations

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    Cited by:

    1. von Sachs, Rainer, 2019. "Spectral Analysis of Multivariate Time Series," LIDAM Discussion Papers ISBA 2019008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Chau, Van Vinh & von Sachs, Rainer, 2017. "Positive-Definite Multivariate Spectral Estimation: A Geometric Wavelet Approach," LIDAM Discussion Papers ISBA 2017002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Hu, Zhixiong & Prado, Raquel, 2023. "Fast Bayesian inference on spectral analysis of multivariate stationary time series," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    4. Robert T. Krafty & Ori Rosen & David S. Stoffer & Daniel J. Buysse & Martica H. Hall, 2017. "Conditional Spectral Analysis of Replicated Multiple Time Series With Application to Nocturnal Physiology," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1405-1416, October.
    5. Beran, Jan & Heiler, Mark A., 2007. "Estimation of a nonparametric regression spectrum for multivariate time series," CoFE Discussion Papers 07/12, University of Konstanz, Center of Finance and Econometrics (CoFE).
    6. Rosen, Ori & Thompson, Wesley K., 2009. "A Bayesian regression model for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3773-3786, September.
    7. Christian Macaro & Raquel Prado, 2014. "Spectral Decompositions of Multiple Time Series: A Bayesian Non-parametric Approach," Psychometrika, Springer;The Psychometric Society, vol. 79(1), pages 105-129, January.
    8. Cadonna, Annalisa & Kottas, Athanasios & Prado, Raquel, 2017. "Bayesian mixture modeling for spectral density estimation," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 189-195.
    9. Segal Mark R, 2008. "Re-Cracking the Nucleosome Positioning Code," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 7(1), pages 1-24, April.
    10. Meier, Alexander & Kirch, Claudia & Meyer, Renate, 2020. "Bayesian nonparametric analysis of multivariate time series: A matrix Gamma Process approach," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    11. Shibin Zhang, 2022. "Automatic estimation of spatial spectra via smoothing splines," Computational Statistics, Springer, vol. 37(2), pages 565-590, April.
    12. Zhang, Shibin, 2019. "Bayesian copula spectral analysis for stationary time series," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 166-179.
    13. Zhang, Shibin, 2016. "Adaptive spectral estimation for nonstationary multivariate time series," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 330-349.
    14. Zhang, Shibin, 2020. "Nonparametric Bayesian inference for the spectral density based on irregularly spaced data," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).

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